Problem: Simplify the following expression: $t = \dfrac{84z + 84}{60z}$ You can assume $z \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $84z + 84 = (2\cdot2\cdot3\cdot7 \cdot z) + (2\cdot2\cdot3\cdot7)$ The denominator can be factored: $60z = (2\cdot2\cdot3\cdot5 \cdot z)$ The greatest common factor of all the terms is $12$ Factoring out $12$ gives us: $t = \dfrac{(12)(7z + 7)}{(12)(5z)}$ Dividing both the numerator and denominator by $12$ gives: $t = \dfrac{7z + 7}{5z}$